A transformation of a higher Gaussian beam in general astigmatic optical systems is described in terms of
rotations in 3D space. This way is simpler than direct Fourier integral calculation and preferable for numerical
simulations. Two examples of optical systems and corresponding transformations, connecting with mode
converter and fractional Fourier transform, are discussed.
The intensity of spiral beams remains unchanged under propagation and focusing neglecting scaling and rotation. The spiral beam with predetermined intensity in the shape of any planar curve can be generated by use of amplitude and phase elements concurrently. We introduce the new method of singular laser fields formation, close to spiral type, by means of pure phase modulation. Our algorithm is based on the well-known Gerchberg-Saxton phase retrieval algorithm and spiral beams optics. It demonstrates fast convergence and some other advantages: phase distributions obtained are stable to spatial resolution changing (it is enough 128 x 128 pixels for some patterns), theoretical energy efficiency is about 85 % with acceptable intensity homogeneity. We demonstrate theoretical results on fields formation in the shape of closed-curves (triangular, square, "snowflake") and open-ended curve (Archimedes spiral) by means of elements on dichromate gelatin. Besides, the example of experiment on micromanipulation with the use of the square-shaped field is presented.
Development of methods for generating of laser beams with predetermined values of intensity and angular momentum distributions is a challenge of great interest for various laser technologies including laser manipulation by microscopic objects. The suggested method oftransformation of laser radiation to complex structure modes in build-up beam rotator interferometer has been theoretically evolved and experimentally tested. Its main advantage over the others is that the method doesn't require complex diffractive optical elements to be used. Experiments were performed using tunable (adjustable) diode laser and interferometer formed by three mirrors. The beam rotation has been achieved by Dove prism inserted into the interferometer. The evolution of the transformed beam was observed with alternation of the prism rotation angle and the injection current of the laser diode.
Structurally stable laser beams with phase singularities that are rotating under propagation (so called spiral beams) have been investigated in various aspects. Some integral invariants of general laser beams and an optical analog of the Steiner theorem in mechanics are presented. Similarity and distinction of spiral beams for different rotation behavior are shown. A usage of spiral beams shaped like a predetermined planar curve applying for construction of phase focusing element is discussed.
A beam propagation through astigmatic square-law waveguides (n(x,y) equals Kx2X2 + Ky2Y2) is investigated by theoretical and experimental means. It is shown that if certain condition between astigmatic value, length of waveguide, wave-front curvature and Gaussian parameters takes place then a Hermite-Gaussian beams transforms into Laguerre-Gaussian beams without residual astigmatism.
In this review some results on spiral beam optics are considered. Spiral beams keep their intensity structure unchanged under propagation except its scale and rotation. Some theoretically calculated spiral beams and the ways of their experimental constructing are presented. A comparison between an example of nonrotating but structurally stable beam and a corresponding spiral beam is performed.
It is known that Laguerre-Gauss beams with indices n equals 0 and nonzero m have a single phase singularity of order m and the intensity shaped as a circumference. In this work a generalization of these beams is proposed, namely, for any closed curve on the plane there exists a family of singular beams depending on a pair of integer-valued parameters, any member of which is structurally stable under propagation and focusing. In particular, when the curve is a circumference Laguerre-Gauss modes and parameters n,m are obtained.